For each of the following examples:

  1. Write out all of the causal pathways from X (treatment of interest) to Y (outcome of interest).
  2. Identify which variable(s) need to be controlled to estimate the causal effect of X on Y. You can use dagitty.net to help you, but you should start trying to recognize these on your own!
  3. Draw the DAGs in r using ggdag. After setting up the dag with dagify() (and specifying exposure and outcome inside dagify), pipe that into ggdag(). Try again piping it instead into ggdag_status() (to highlight what is X and what is Y). Try again piping it instead into ggdag_adjustment_set() to show what needs to be controlled.

Don’t forget to install ggdag!

Question 1

Part I

Pathways:

  1. \(X \rightarrow Y\) (causal, front door)
  2. \(X \leftarrow Z \rightarrow Y\) (not causal, back door)

Part II

\(Z\) needs to be controlled for, since it is opening a backdoor path.

Part III

dag1 <- dagify(Y ~ X + Z,
       X ~ Z,
       exposure = "X",
       outcome = "Y")

dag1 %>%
  ggdag_status(seed = 1)+
  theme_dag_blank()

dag1 %>%
  ggdag_paths(seed = 1)+
  theme_dag_blank()

dag1 %>%
  ggdag_adjustment_set()+
  theme_dag_blank()

Question 2

Part I

Pathways:

  1. \(X \rightarrow Y\) (causal, front door)
  2. \(X \rightarrow M \rightarrow Y\) (causal, front door)

Part II

Nothing should be controlled for, since \(M\) is a mediator, and part of the effect of \(X\) on \(Y\)

Part III

dag2 <- dagify(Y ~ X + M,
       M ~ X,
       exposure = "X",
       outcome = "Y")

dag2 %>%
  ggdag_status(seed = 1)+
  theme_dag_blank()

dag2 %>%
  ggdag_paths(seed = 1)+
  theme_dag_blank()

dag2 %>%
  ggdag_adjustment_set()+
  theme_dag_blank()

Question 3

Part I

Pathways:

  1. \(X \rightarrow Y\) (causal, front door)
  2. \(X \leftarrow A \rightarrow Z \rightarrow Y\) (not causal, back door)
  3. \(X \leftarrow A \rightarrow Z \leftarrow B \rightarrow Y\) (not causal, back door)

Part II

Backdoor path 3 is closed by the collider at \(Z\). Backdoor path 2 remains open, so we need to control for \(A\). (If we blocked \(Z\) to close path 2, that would open up backdoor path 3!) Only \(A\) should be controlled for.

Alternatively, we could control for \(B\) and \(Z\).

Part III

dag3 <- dagify(Y ~ X + Z + B,
       Z ~ B + A,
       X ~ A,
       exposure = "X",
       outcome = "Y")

dag3 %>%
  ggdag_status(seed = 1)+
  theme_dag_blank()

dag3 %>%
  ggdag_paths(seed = 1)+
  theme_dag_blank()

dag3 %>%
  ggdag_adjustment_set()+
  theme_dag_blank()

Question 4

Part I

Pathways:

  1. \(X \rightarrow Y\) (causal, front door)
  2. \(X \rightarrow C \rightarrow Y\) (causal, front door)
  3. \(X \leftarrow A \rightarrow Z \rightarrow B \rightarrow Y\) (not causal, back door)

Part II

Path 2 is a front door path we want to leave open. Backdoor path 3 is closed by the collider at \(Z\). Nothing needs to be controlled for!

Part III

dag4 <- dagify(Y ~ X + B + C,
       Z ~ B + A,
       X ~ A,
       C ~ X,
       exposure = "X",
       outcome = "Y")

dag4 %>%
  ggdag_status(seed = 1)+
  theme_dag_blank()

dag4 %>%
  ggdag_paths(seed = 1)+
  theme_dag_blank()

dag4 %>%
  ggdag_adjustment_set()+
  theme_dag_blank()

Question 5

Part I

Pathways:

  1. \(X \rightarrow Y\) (causal, front door)
  2. \(X \rightarrow Z \rightarrow Y\) (causal, front door)
  3. \(X \rightarrow Z \leftarrow A \rightarrow Y\) (not causal, back door)
  4. \(X \rightarrow Z \leftarrow B \rightarrow A \rightarrow Y\) (not causal, back door)

Part II

Path 2 is a front door path we want to leave open. Backdoor path 3 is closed by the collider at \(Z\). Backdoor path 4 is closed by the collider at \(Z\). We don’t want to control for anything!

Part III

dag5 <- dagify(Y ~ X + Z + A,
       Z ~ X + A + B,
       B ~ A,
       exposure = "X",
       outcome = "Y")

dag5 %>%
  ggdag_status(seed = 1)+
  theme_dag_blank()

dag5 %>%
  ggdag_paths(seed = 1)+
  theme_dag_blank()

dag5 %>%
  ggdag_adjustment_set()+
  theme_dag_blank()